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1 Journal of Theoretical and Applied Mechanics

1 2025

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Global behaviors of parameterized solution domain and basins of attraction of star herringbone gear transmission system

Lin He, Guo Jiamin, Li Yingjie, Cheng Xiaole, Hong Ling

Journal of Theoretical and Applied Mechanics

2025

Vol. 63 nr 2

289--306

The analysis of global behaviors is quite essential for the prediction of the potential dynamical vibration of the geared system. A novel meshing stiffness formula approximated to rectangular wave was proposed utilizing an odd harmonic superposition, the distribution maps of the parameterized solution domain and basin of attraction of the star herringbone gear transmission system were calculated containing various periodic regions and then validated. The analysis of the joint probability density indicates that transformations occurred on the portrait structure of attractors during the evolution into chaos. In addition, with discretization techniques and cell mapping methodology, the two-dimensional parameterized solution domain, as well as overall distributions of periodic and chaotic domains hidden in the basins of attraction were identified. Subsequently, the stochasticity of the damping ratio produced in normal distribution is analyzed, which presents that the attractor will experience perturbations before reaching a steady-state, while the periodicity of the attractor is significantly weakened. By the comparison of evolution behaviors, the distributions of periodic basin of attraction have little variations, but it caused some scattered periodic cells which mixed in the original domains, resulting in the deterioration of the steady-state to the system.